Identifier
-
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St000054: Permutations ⟶ ℤ
Values
[1,0] => [1,0] => [1] => 1
[1,0,1,0] => [1,0,1,0] => [1,2] => 1
[1,1,0,0] => [1,1,0,0] => [2,1] => 2
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,2,3] => 1
[1,0,1,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => 1
[1,1,0,0,1,0] => [1,1,0,0,1,0] => [2,1,3] => 2
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [1,3,2] => 1
[1,1,1,0,0,0] => [1,1,1,0,0,0] => [3,2,1] => 3
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 1
[1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 1
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 2
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 1
[1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 2
[1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 1
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 3
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 2
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 1
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 2
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 2
[1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 2
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 2
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 2
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 3
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 3
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 2
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 4
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 3
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
>>> Load all 824 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => 10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 8
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => 8
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8,9,10] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8,9,10] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => 5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => 7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => 10
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 8
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 4
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 8
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 4
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9,12,11] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => 4
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => 2
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => 4
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => 6
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => 2
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => 4
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,1,1 8,4,1,1 23,12,5,1,1 71,36,17,6,1,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 3\ q + q^{2} + q^{3}$
$F_{4} = 8\ q + 4\ q^{2} + q^{3} + q^{4}$
$F_{5} = 23\ q + 12\ q^{2} + 5\ q^{3} + q^{4} + q^{5}$
$F_{6} = 71\ q + 36\ q^{2} + 17\ q^{3} + 6\ q^{4} + q^{5} + q^{6}$
Description
The first entry of the permutation.
This can be described as 1 plus the number of occurrences of the vincular pattern ([2,1], {(0,0),(0,1),(0,2)}), i.e., the first column is shaded, see [1].
This statistic is related to the number of deficiencies St000703The number of deficiencies of a permutation. as follows: consider the arc diagram of a permutation $\pi$ of $n$, together with its rotations, obtained by conjugating with the long cycle $(1,\dots,n)$. Drawing the labels $1$ to $n$ in this order on a circle, and the arcs $(i, \pi(i))$ as straight lines, the rotation of $\pi$ is obtained by replacing each number $i$ by $(i\bmod n) +1$. Then, $\pi(1)-1$ is the number of rotations of $\pi$ where the arc $(1, \pi(1))$ is a deficiency. In particular, if $O(\pi)$ is the orbit of rotations of $\pi$, then the number of deficiencies of $\pi$ equals
$$ \frac{1}{|O(\pi)|}\sum_{\sigma\in O(\pi)} (\sigma(1)-1). $$
This can be described as 1 plus the number of occurrences of the vincular pattern ([2,1], {(0,0),(0,1),(0,2)}), i.e., the first column is shaded, see [1].
This statistic is related to the number of deficiencies St000703The number of deficiencies of a permutation. as follows: consider the arc diagram of a permutation $\pi$ of $n$, together with its rotations, obtained by conjugating with the long cycle $(1,\dots,n)$. Drawing the labels $1$ to $n$ in this order on a circle, and the arcs $(i, \pi(i))$ as straight lines, the rotation of $\pi$ is obtained by replacing each number $i$ by $(i\bmod n) +1$. Then, $\pi(1)-1$ is the number of rotations of $\pi$ where the arc $(1, \pi(1))$ is a deficiency. In particular, if $O(\pi)$ is the orbit of rotations of $\pi$, then the number of deficiencies of $\pi$ equals
$$ \frac{1}{|O(\pi)|}\sum_{\sigma\in O(\pi)} (\sigma(1)-1). $$
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
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